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CHAPTER 7

CHAPTER 7. CARRIER LIFETIMES. 7.1 INTRODUCTION. Lifetime: Generation lifetime, recombination lifetime. Occur in bulk: lifetime τ g , τ r . . Occur in surface: surface velocity s g , s r .

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CHAPTER 7

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  1. CHAPTER 7 CARRIER LIFETIMES

  2. 7.1 INTRODUCTION • Lifetime: Generation lifetime, recombination lifetime. • Occur in bulk: lifetime τg, τr.. • Occur in surface: surface velocity sg, sr. • The measured lifetime are always effective values consisting both components.

  3. Recombination and Generation (a) Forward-biased and (b) reverse-biased junction.

  4. 7.2 RECOMBINATION LIFETIME-SURFACE RECOMBINATION VELOCITY • Consider p-type semiconductor in this chapter. • Consider minority electrons. • Consider linear, quadratic, and third-order terms.

  5. RECOMBINATION LIFETIME-SURFACE RECOMBINATION VELOCITY (7.1) (7.2) n=no+Δn, p=po+Δp, no<<po, Δn=Δp. (7.3) (7.4)

  6. Recombination mechanisms: (a) SRH, (b) radiative, (c) Auger.

  7. (7.5) (7.6) (7.7) (7.8) (7.9)

  8. (7.10) low-level injection (ll):Δn<<po, high-level injection (hl): Δn>>po. (7.11) (7.12) (7.13)

  9. Table 7.1 Recombination Coefficient

  10. Recombination Lifetime Versus Majority Carrier Density Recombination lifetime versus majority carrier density for p-Si [Cp=1.1×10-30 cm6/s (dashed lines), Cp =10-31cm6/s (solid lines)] and for n-Si (Cn=2.8×10-31 cm6/s). Data from Ref. 10.

  11. SRH (multi-phonon) recombination (7.14) (7.15) (7.16) (7.17) (7.18) (7.19)

  12. sr Versus Injection Level η sr Versus Injection Level η As a function of σpsfor Nit=1010cm-2, pos=1016cm-3, ETs=0.4eV, σns=5×10-14cm2. Data from ref. 15

  13. For heavily doped Si, Auger recombination dominates the carrier lifetime. • For lightly doped Si, SRH (multi-phonon) recombination dominates the carrier lifetime. • Radiative recombination plays almost no role in Si, but is important in direct bandgap material like GaAs.

  14. 7.3 GENERATION LIFETIME-SURFACE GENERATION VELOCITY • Each of the recombination process has a generation counterpart. SRH recombination --- Thermal generation Radiative recombination --- Optical generation Auger recombination --- Impact ionization • When pn>ni2 recombination dominates, when pn<ni2 generation dominates. • The smaller the pn product, the higher is the generation rate.

  15. (7.20) (7.21) Usually, τg>τr. For Si τg≒(50~100)τr. (7.22) when psns<ni2 (7.23) For ET≠Ei, sr > sg.

  16. 7.4 RECOMBINATION LIFETIME-OPTICAL MEASUREMENTS The continuity equation for uniform ehp generation and zero surface recombination (7.24) n(t)/t = G – R = G – n(t)/ τeff τeff(n) = n(t)/ [G(t) –dn(t)/d(t)] (7.25) In the Transient Photoconductance Decay (PCD) method, with G(t) << dn(t)/d(t) τeff(n) = – n(t)/ dn(t)/d(t) (7.26)

  17. In the steady-state method, with G(t) >> dn(t)/d(t) τeff(n) = n(t)/ G (7.27) The excess carrier density for low level injection is given by Δn(t)= Δn(0)exp(-t/τeff) (7.28) (7.29) τB is the bulk recombination lifetime, D the minority carrier diffusion constant under ll injection or the ambipolar diffusion constant under hl injection, d the sample thickness.

  18. For thick samples τeff ~ τB. For thin samples τeff depends on d and sr. Effective lifetime versus wafer thickness as a function of surface recombination velocity. D=30cm2/s.

  19. (7.30) Two limiting cases are of particular interest: sr  0 gives tan(d/2)d/2 and sr   gives tan(d/2) or d/2/2 (7.31) • For Sr~0, plot 1/τeff vs. 1/d, the slope is 2sr, the intercept is 1/τB • For Sr~∞, plot 1/τeff vs. 1/d2, the slope is πD2, the intercept is 1/τB.

  20. Determination of bulk lifetime, surface recombination velocity, and diffusion coefficient from lifetime measurements.

  21. The above discussions holds for samples with one dimension much smaller than the other two dimensions. For samples with none of the three dimensions (a, b, and c) very large, then for sr~ ∞ (7.32) (7.33) (7.34) (7.35) (7.36)

  22. Calculated normalized excess carrier density versus time as a function of surface recombination velocity. d=400μm, α=292 cm-1 (optical absorption coefficient).

  23. 7.4.1 Photoconductance Decay (PCD) Schematic diagram for photoconductance decay measurements. In PCD, the conductivity   = q (nn+ pp) (7.37) n=n0+n, p=p0+p under low level injection n = p, the excess carrier density is related to the conductivity by n=   / q (nn+ pp) (7.38)

  24. Schematic diagram for photoconductance decay measurements. (7.39) (7.40) (7.41) Where Δg =ΔσA/L.

  25. For constant voltage method, choose R smaller than the sample resistance, in ll case RΔg<<1 or ΔV<<Vo, then (7.42) For constant current method, R is very large, if rdkΔg<<1 or ΔV/ Vo/<<rdk /R, then (7.43)

  26. For ΔV to be proportional to Δn, it is necessary that ll injection must prevail, otherwise corrections must be applied. • The contacts should not inject minority carriers, nor should they raise sample temperature. • The electric field in the sample should be held at E≦0.3/(μτr)1/2,μ is minority carrier mobility. • The excitation light should be penetrating through the sample.

  27. PCD Measurement Schematic for Contactless (a) RF bridge measurement (b) Microwave Reflectance Measurement

  28. Low Sr can be achieved by: • Oxidized Si surface, Sr=20cm/s. • Immersing Si in HF (Sr=0.25cm/s), in iodine/methanol (Sr=4cm/s). • Low temperature SiN remote plasma CVD deposition (Sr=4-5cm/s). • Inorganic sulfides passivation on GaAs (Sr=1000cm/s), In the microwave reflection method P / P = C  (7.44)

  29. 7.4.2 Quasi-Steady-State Photoconductance (QSSPC) The sample is illuminated with a flash lamp with a ms decay time, the sample is under quasi-steady-state during the measurement as the light intensity varies from the maximum to zero. The generation rate is G = f / d (7.45) G(t) = 0 for t  0; G0exp(-t/flash) for t > 0 (7.46) For eff < flash , the solution of Eq. (7.25) is n(t)=eff/(1-eff /flash )G0(exp(-t/flash )-exp(-t/eff) (7.47)

  30. Effective Recombination Lifetime Versus Injection Carrier Density Obtained with the QSSPC technique. Adapted from ref. 37.

  31. 7.4.3 Short-Circuit Current / Open-Circuit Voltage Decay (SCCD/OCVD) For the short-circuit current, (7.48a) (7.48b) For the open-circuit voltage (7.49)

  32. The current decays exponentially with time, the time constant depends on excess carrier density. • The voltage decay is influenced by the junction RC time constant. This effect is reduced by measuring the small-signal voltage decay with a steady-state bias light to reduce R. • For samples with thickness much larger than the minority carrier diffusion length, sr is no longer important • Isc, Voc ~ (exp(-t/τB))/(t1/2) (7.50)

  33. 7.4.4 Photoluminescence Decay (7.51) • Direct band gap material has larger PL density than indirect band gap • material. • It becomes complicate when self-absorption occurs . (7.52) • The first term is the non-radiative lifetime,γ is the photon recycling • factor. • Self-absorption is not important for indirect semiconductor.

  34. 7.4.5 Surface Photovoltage (SPV) Sample cross section for SPV measurements. The optically transparent, electrically conducting contact to the left of the sample allow light to reach the sample and the voltage to be measured. • The surface scr is induced by surface charges, not due to a bias voltage. • The incident light wavelength is varied, the sample back is kept in dark. • Some minority carriers diffuse toward the illuminated surface, building a SPV which is proportional to Δn(W).

  35. SPV method is used to determine the minority carrier diffusion length. • To simplify data extraction, we need • Undepleted wafer much thicker than Ln • Thescr width smaller than Ln • α(d-W)>>1>> αW, α the absorption coefficient • Sample diameter > sample thickness (7.53) The diffusion equation solution is (7.54)

  36. The Δn(W) is related to the voltage by (7.55) which yields (7.56) Vspv is proportional to Δn for Vspv<0.5kT/q In constant surface photovoltage method, Vspv=const, Δn(W) is constant, for different wave lengths with different α, adjust the photon flux density to obtain constant Vspv, this yields

  37. (7.57) Plot Φ vs. 1/α, the intercept is Ln and the slope is related to s1. In constant photon flux density method, (7.58) Plot 1/ Vspv vs. 1/α, the intercept is Ln.

  38. (a) Constant voltage, (b) constant photon flux SPV plots for Si samples.

  39. The condition W<<Ln is usually true for single-crystal Si, yet, for GaAs and amorphous Si this condition is not satisfied, then the intercept is given as (7.59) The relation between λ and α is important for the accuracy of SPV method For Si, λ=0.7~1.1μm. (7.60) For GaAs, λ=0.75~0.87μm. (7.61) For InP, λ=0.8~0.9μm. (7.62) For Si. (7.63)

  40. 7. 4. 6 Steady-State Short-Circuit Current The sample should be a pn junction or Schottky diode.The Jsc is measured with varying wavelength. Measurement schematic for (a) the short-circuit current diffusion length measurement method, (b) for the ELYMAT double surface method.

  41. (7.64) For an n+p diode the second term is negligible. (7.65) Adjust Φ such that Jsc is kept constant. (7.66) Where C1=Jsc/q(1-R)Ln,plot Φ vs. 1/α. (7.67) Or write Where X=q(1-R) Φ/Jsc, plot 1/α vs. (X-1).

  42. Electrolytical metal tracer method: IF: short penetration depth, moderate diffusion length,negligible back surface recombination. IR: penetrating light, low front surface recombination. (7.68a) (7.68b) A is the area, sf is the front surface recombination velocity.

  43. 7.4.7 Free Carrier Absorption (b) (a) • Schematic free carrier absorption arrangement, • (b) schematic for lifetime mapping.

  44. Pump beam energy hυ>Eg, probe beam energy hυ>Eg. The transmitted photon flux is (7.69) d is the sample thickness, αfc is free carrier absorption coefficient, R the reflectance. For n-type semiconductor Kn~10-18cm2/μm2, Kp~(2-2.7)10-18cm2/μm2. fc=Kn2n (7.70)

  45. The change in a transmitted pulsed beam is (7.71) The change in the absorption coefficient is (7.72) Δn is related to the minority carrier lifetime. The fractional change in transmitted flux is (7.73)

  46. Knowing the laser generation rate G’=(1-R)(cm-2s-1) and the sample thickness d, the effective lifetime is eff = dn/G’ (7.74) Free carrier absorption lifetime map The black body emits over a wide wavelength range with a peak at peak = 3000/T m (7.75)

  47. 7.4.8 Electron Beam Induced Current (EBIC) E/Eehp=Nehp+γ(Ebs/Eehp) (7.76) Ebs is the mean backscattering electron energy, Eehp~3.2Eg, =3.64eV for Si. γis the backscattering coefficient. The electron penetration depth is ρis the semiconductor density. The generation volume is pear shaped for Z<15. for 15<Z<40 a sphere, for Z>40 a semispherical. (7.77)

  48. Electron Beam Induced Current Assume a sphere volume of (4/3) π(Re/2)3, the generation rate is (7.78) For Si with a beam current of 10-10A. Eehp=3.64eV, E=104eV, G=3X1024 ehp/cm3.s IEBIC can be collected by a junction. The beam position and energy can be changed. G’=IbNehp/q. (7.79)

  49. Conventional EBIC implementation, (b) depth modulation by electron beam energy. In figure (b), (7.80) For high Sr, (7.81)

  50. 7.5 RECOMBINATION LIFETME-ELECTRICAL MEASUREMENTS pn junction I-V curve showing the space-charge and quasi-neutral region currents.

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